blue_moonI am rather excited today because I am going to be interviewed by Sir David Frost!

However, the good news is that my excitement has not caused me to forget about the Friday puzzle…

Imagine that you had a piece of paper, 0.1mm thick, that could be folded in half as many times as you like.Β  How many times would you need to fold the paper before it was thick enough to reach the Moon?

As ever, feel free to leave comments saying if you think you solved it and how long it took, but please don’t post your solution.Β  I have also given a list of possible answers below – please vote for the one that you believe is closest to the correct figure.

120 comments

    1. *argh* that would have been a real eventuality to have a test.. Chose the old plain-vanilla zero-counting and rough estimate πŸ™‚

    2. hey ben do you go to meadowlane????? :O:O:O:O:O:O:O:O:O:O:S:S:S:S:S:S:S:S oh ben and will

    1. It does say “imagine you have…..that could be folded in half as many times as you like”. I think that covers it.

  1. Hmmm. I too used Wolfram Alpha, but I’m not convinced there’s not some trick here I’m missing.

    I’m assuming the whole “could be folded in half as many times as you like” thing counters the whole “there’s only a certain number of times you can practically fold a piece of paper in half” thing.
    So I will be interested to see the answer on Monday.

    1. Well, it should be self-evident in reality that a piece of paper could not be folded in half such that the thickness can exceed the length/width of the paper unless the corresponding dimension is reduced below the thickness. To reach the Moon, it would be *well* below the starting size. I leave it to the reader to calculate the volume of a standard sheet of paper and compare it to that of the radius of a cylinder long enough to reach the same disance.

  2. It took a couple of minutes, but that was just looking at the RSS feed and not realising there were multiple choice answers.

  3. I did it in my head, and I am 100% confident I got the right answer. It’s pretty easy if you know some trivial rules of thumb about powers of two. And having a rough idea about the distance to the moon helps too πŸ˜‰

    /Z

  4. I had to look up the earth-moon distance on Wikipedia (although I didn’t think to just deduce it from the options available…) but from there, seconds to do it mentally, and about 2 minutes to work out where the hell I’d lost a factor of ~1000

  5. Knowing the math and approx distance to the moon I chose an answer in about 10 secs based on a very rough estimate. Took less than a minute then to double check on calculator just to be sure I was right. πŸ™‚

    when I saw the picture of the moon, I thought it was going to be the ol’ question of which coin held at arms length would just cover a full moon as a question of psychology rather than math πŸ™‚

    1. ah! a matching one πŸ˜‰ countig ’til the date and maybe the same rough estimate took a quarter minute. was a too good fit not to vote – and validated later with calcs help.
      Even the first guess is the same…

  6. I used the calculator on my computer. (It’s always annoyed me that scientific calculators use the notation x squared to raise the name in the display to the power of 2; but y to the power x to raise the same number to the power of the number you enter next.)

  7. You didn’t specify the dimensions of the paper, only it’s thickness.
    Can I not then say I’ll use a piece of paper sufficiently large to make any of those answers legitimate, simply by not orienting it in such a way it’s thickness at all matters?
    This of course assumes you can fold a piece of paper a theoretical infinite number of times without it either breaking or becoming thicker than is possible to make a proper fold.

    Finally if we use a standard piece of A4, are there even enough atoms to reach the moon contained with in the paper?

    This question seems too vague to answer certainly without making several unrealistic assumptions.

    I was going to answer 0 and use a piece of paper exactly the length from here to the moon, but that wasn’t an option, so my answer which I won’t say here, was chosen arbitrarily.

    1. Yeah, but it says “thick enough to reach the Moon”. I think that means you have to do it by folding. The paper is imaginary, it doesn’t have to obey the laws of physics. Of course you have to make unrealistic assumptions, but the question isn’t vague in the least.

  8. Whoa, way to over-analyse the question, Dan

    I think Richard is just asking us to think about powers of two, and (the surprising) number you need to reach that distance.

  9. The problem was intuitively obvious (mathematically speaking). It took about 2 minutes to solve… but it is a standard Physics problem – demonstrating the power of doubling.

  10. Isn’t the moons orbit elliptical? (sorry, just trying to hide my ignorance of basic maths with my knowledge of basic astronomy).

  11. Had to use a calculator, and about a minute. At first I thought the choices were all too small, but, as Jon Carnes above said, it just shows “the power of doubling”.

  12. I suppose, pedantically speaking, the paper will never be thick enough to reach the moon, as its thickness isn’t changed by folding….

    On a similar note, it’s a fairly big assumption that a 0.1mm piece of paper folded in half makes exactly 0.2mm (and more so as the number of folds increases).

    “How many times would you need to cut the stack in half, and stick the two halves together, before the stack could reach the moon”

    But interpreting the question in the spirit in which I think it was meant, about 2 minutes with a calculator and Google.

    1. “Its thickness isn’t changed by folding” was my first answer too πŸ˜‰
      Thus the only answer is “infinity”!

  13. less than 30 secs, using spreadsheet, if I got the right answer.
    About an hour, re-checking my answers and working out where I went wrong, if indeed I got it wrong.

  14. Nice to find a potentially ‘do-able’ puzzle for me. Not used basic calculator for weeks πŸ™‚

    Please let me know whereyou sourced this awsome sheet of physics-defying paper.

  15. I’m not a physicist but … wouldn’t the paper at some point extend far enough into zero-gravity space that it could float to the moon?

  16. No idea how to solve this with math, so I used a calculator. I didn’t do it *exactly* — meaning my answer wasn’t one of the multiple choices — but I also didn’t do it wrong, so I know more of less what the answer should be. Very cool.

  17. I made a semi wild guess in about twenty seconds, guessing the answer would be counterintuitivly on the low side.

    And I’m interpreting “folding in half” as “doubling in thickness”, since it would otherwise become an unfoldible lump of paper after maybe 6-8 folds. Maybe it would be easier to fold it once so it fits in an envelope and mail it to NASA, with a request that it accompanies the next moon mission.

  18. If I did my math right (and using the limiting equation from Benjamin’s link)…you would need that paper to be in the form of a strip long enough to circle the Earth 25 trillion times. mind=boggled

  19. 4 is a little – low i guess – considering it is practically only possible to fold paper 6 times, I don’t reckon the number to be very high, though

  20. Took me a couple of minutes and my answer was an exact match to one of the choices so I was proud of myself. But then again it’s not exactly rocket science (unless you’re really good at origami).
    Done on the Mac’s calculator widget and was surprised it held the whole number in millimeters. (yup, not being a mathematician I had to do it the long way)

  21. Another physicist, another 10s or so in my head. As has been commented, knowing some tricks of powers of 2 and knowing the distance to the moon helps.

    I think being a physicist means that you know when to include added complications and when to stick with the simple approximations which get you an acceptable answer. Yes, the moon’s orbit is elliptical but the variation is less than the error introduced by doing the maths in my head so I know it’s an irrelevance. And so on.

  22. I’m not going to question the intelligences of anyone here, I just wonder how many people that answered forgot to convert out of mm? Classic mistake from my own physics studies, but I remembered this time.

    1. Glad that someone brought Mythbusters up. πŸ™‚ That is actually paper, just so much of it that it might not look like paper…

  23. Yup – without knowing how far away the moon is I’ll go with the 4th one…

    Frost ey? Well, my one piece of advice is that if you had anything to do with Watergate just deny everything and never apologise to the American public, otherwise history may end up judging you badly… good luck!

  24. Had to look up the distance to the moon but after that just a guess and a quick check on a calculator – 2 minutes. Remembered the story of the grain of rice on a chessboard from schooldays.

  25. Got it in a couple of minutes. Had to find out how far away the moon is, then did a quick and dirty formula in excel to get me the correct answer.

  26. This is like making puff pastry. Just in case some of you math experts out there don’t know what I’m talking about, you make puff pastry by folding dough over butter, rolling it out, folding it again, chilling it and doing it over and over again. The chilled butter between all those dough layers is what makes the dough puff up in the baking. Fortunately, the layers don’t have to reach to the moon. More than you wanted to know? I don’t know the formula nor how to do spreadsheets. My husband, who plays with numbers all day as a budget analyst, figured it out in about one minute. He thinks he has the right answer. Me? I’m just baking.

    1. Now that’s what I call a reply !
      … much better than all that wittering on about “you can’t fold paper that often”…

      I couldn’t think of any mathematical short cuts so did it with some messy Excel.

      Earlier on Scott mentioned homophones so (tenuous connection) I suppose when I see the easy maths to work it out I’ll be saying …
      “dough !”

      πŸ˜‰

  27. I wrote mine out by hand and discovered some neat numbers trends I’d never noticed before. I hated math in school. My solution was not one of the choices, but within 10 of one…I guess I’ll see…

  28. Wow, I can’t believe my first uneducated guess was correct, but I should have known. First guess=Instantaneously. Math to confirm=less than a minute with tools at hand.

  29. My father, who never got past the sixth grade back in the teens, was a genius at math. Honestly. I grew up encountering problems like these to solve. And up until a couple of months ago i could “compete” in your quizes. No mas. Blessings.

  30. My father was a genius at math although he never got past the sixth grade in school. I grew up being presented with problems like these to solve. And up until a couple of months ago I could hold my own.
    Now, it doesn’t matter. Blessings,

  31. Since I am imagining this and I can fold it as much as I like…. well I’d say four times…. fits in my pocket better that way. Hop a flight to Fl and take the next space shuttle. Then go on a very, very long space walk after being given a nice shove out the door and land on the moon and place my paper there and put a moon rock on it after making sure my name isn’t on it so I won’t be charged with littering. I like to problem solve by thinking out of the box….. it’s more fun that way…… :}

  32. About a minute. Thought about logarithms, decided I didn’t feel like them at 5am so googled “Earth to moon”, converted to millimetres then googled “powers of 2”. Not that I’m addicted to Google or anything.

  33. I bet Planck knows this one! Even if I could find that answer, I think I’d be clumsy enough to just tear it apart, or lose it, before I even got any further. Marvin the Paranoid Android would comment “what’s the point, anyway”.

    However!, my answer will be “one billion times” – because it sounds like such a nice round number, and for its high improbability level!

    And they say there’s water up there! Normality has been restored.

  34. Hi all -took about two min to get the distance and numeric sequence upon foldoing to get a value close to the proper distance (which I had go google to start the calculation). Used my HP 32S_II power function key to ball park to the closest answer…. Hmmn – it was fun !

  35. I believe that none of the indicated selections are even vaguely correct, but I did as instructed and chose the closest one.
    I m hampered by the fact that I am a mathematician, and so may be overly pedantic about such matters, sucking the fun out of these quizzes like a numeric vampire!

  36. I thought “this is a piece of cake” and put the numbers up, checked the distance to the Moon, worked it out in under a minute, and ended up with something that didn’t match any of the alternatives….

    Took me about ten minutes of mistake-searching to realize I had completely messed up the order of magnitude of a millimetre. πŸ˜‰

  37. It took me about a minute to calculate it in my head (which, as a few people have said is easy if you know the distance to the moon and a bit about powers of two), without looking at the choices. Had I known about the choices it would probably have taken me 10 seconds or so.

  38. why is it that the size of the paper has nothing to do with this puzzle? that is the first thing i thought about and the only thing on my mind after i read the puzzle….what size paper are you talking about?

  39. This business about only being able to fold paper a certain number of times: I think there have been sufficient demonstrations to show that there’s no ABSOLUTE limit, but that it depends on the type and size of the paper too. The way the question is framed, we are not told about the type of paper or any limit to its size, so … just do the maths.

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